Evaluating route to impact convergence of the harmonic balance method for piecewise-smooth systems. (June 2023)

• Record Type: Journal Article
• Authors: Saunders, B.E.; Kuether, R.J.; Vasconcellos, R.; Abdelkefi, A.
• Is Part Of: International journal of non-linear mechanics. Volume 152(2023)
• Publication Date: 2023-06
• Subjects: Harmonic balance -- Convergence analysis -- Isolas -- Piecewise-smooth -- Floquet stability; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2023.104398
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: In this work, we investigate the applicability of the harmonic balance method (HBM) to predict periodic solutions of a single degree-of-freedom forced Duffing oscillator with freeplay nonlinearity. By studying the route to impact, which refers to a parametric study as the contact stiffness increases from soft to hard, the convergence behavior of the HBM can be understood in terms of the strength of the non-smooth forcing term. HBM results are compared to time-integration results to facilitate an evaluation of the accuracy of nonlinear periodic responses. An additional contribution of this study is to perform convergence and stability analysis specifically for isolas generated by the non-smooth nonlinearity. Residual error analysis is used to determine the approximate number of harmonics required to get results accurate to a given error tolerance. Hill's method and Floquet theory are employed to compute the stability of periodic solutions and identify the types of bifurcations in the system. Highlights: Applicability of the HBM for Duffing oscillator with freeplay nonlinearity is investigated. HBM results are compared to time-integration results to evaluate the accuracy of nonlinear periodic responses. Stability analysis specifically for isolas generated by the non-smooth nonlinearity is performed. Residual error analysis is used to determine the approximate number of harmonics. Hill's method and Floquet theory are employed to identify the types of bifurcations in the system.